Frank Lampard will join MLS side New York City FC at the end of this season. Photograph: Peter Powell/EPA

Manchester City have admitted making mistakes regarding Frank Lampard’s status, with the club moving to clarify he never signed a two-year deal with New York City FC and so the midfielder was never on loan from the MLS franchise. Instead City say Lampard agreed “a head of terms commitment” with NYCFC that began on 1 January.

Lampard’s precise agreement with NYCFC, City’s sister club, has been unclear after it emerged last week the 36-year-old was never signed by the manager, Manuel Pellegrini, on a temporary basis despite the champions stating this was the case on their website.

A clarification issued on Friday by the club said: “The statement on the NYCFC website in July saying Lampard’s two-year contract took effect from Aug 1, 2014 was a mistake. [The] initial statement on City’s website that it was a loan was also an error.”

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Pellegrini refused to be drawn when asked on Friday how embarrassing the clarification is for City. “I think it’s an issue which is finished,” he said. “Frank now is here. I know that there a lot of different opinions about Frank about that. I respect all of them, but the decision is taken already and Frank will stay here until the end of the season.

“I repeat I don’t want to continue talking about that thing because it’s finished. All the different problems have another problem inside of that problem. I think at this moment it’s finished.”

The Premier League, meanwhile, is unhappy with City’s insistence that Lampard signed on a six-month contract up to New Year’s Eve and the governing body urged the club to confirm he had signed a 12-month deal starting in August with a break clause on 31 December that had to be removed for the 36-year-old to stay with City, which it was. Contracts of fewer than 12 months are not allowed under Premier League rule T11.The Premier League on Thursday indicated that Lampard had signed a one-year contract at City and that a break clause was removed on New Year’s Eve to allow him to stay at the club, but City’s statement on Friday contradicted this. “There was never a break clause in Lampard’s contract dated 31 December - [there was a] short-term contract with City [that] only ran to Dec 31,” it said before clarifying his agreement with NYCFC. “There was a head of terms commitment from Lampard to join NYCFC from Jan 1, 2015. That was extended to the end of this season. Any contract with NYCFC will now take effect from July 1, 2015.”

The Premier League statement said: “Frank Lampard is registered as a Manchester City player until the end of the 2014-15 season. The Premier League has sought and received assurances from Manchester City that there is no agreement in place between the club or City Football Group with New York City FC relating to the player,” it said.

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Addressing this, City’s said: “The Premier League statement is correct but was a very specific, legal phrasing. Might seem confusing to laymen like us but was agreed by PL lawyers and is right.”

Lampard’s arrival at City was a surprise given the statement he made on 27 July on “joining” NYCFC. “I didn’t want to play anywhere else in England because I had been so affiliated with one club,” he said. “So it made sense for me to move.”